On sufficient conditions of locality for hierarchies of symmetries of evolution systems

We present sufficient conditions ensuring the locality of hierarchies of symmetries generated by repeated commutation of master symmetry with a seed symmetry. These conditions are applicable to a large class of (1+1)-dimensional evolution systems. Our results can also be used for proving that the time-independent part of a suitable linear-in-time symmetry is a nontrivial master symmetry and hence the system in question has infinitely many symmetries and is integrable.